Interfacial electronic states and self-formed asymmetric Schottky contacts in polar α-In2Se3/Au contacts

In recent years, the two-dimensional (2D) semiconductor α-In2Se3 has great potential for applications in the fields of electronics and optoelectronics due to its spontaneous iron electrolysis properties. Through ab initio electronic structure calculations and quantum transport simulations, the interface properties and transport properties of α-In2Se3/Au contacts with different polarization directions are studied, and a two-dimensional α-In2Se3 asymmetric metal contact design is proposed. When α-In2Se3 is polarized upward, it forms an n-type Schottky contact with Au. While when α-In2Se3 is polarized downward, it forms a p-type Schottky contact with Au. More importantly, significant rectification effect is found in the asymmetric Au/α-In2Se3/Au field-effect transistor. The carrier transports under positive and negative bias voltages are found to be dominated by thermionic excitation and tunneling, respectively. These findings provide guidance for the further design of 2D α-In2Se3-based transistors.

Ferroelectric materials, which exhibit the spontaneous and reversible polarization, have great potential in a wide range of applications, such as non-volatile memory 1,2 , field-effect transistors 3 , and optoelectronic devices 4,5 .With the increasingly urgent need for device miniaturization, it is necessary to further explore ultrathin or nanoscale ferroelectric materials.However, the conventional perovskite ferroelectric materials, such as Pb(Zr,Ti) O 3 6 , BaTiO 3 7 , and BiFeO 3 8 , suffer from the size effect.Due to the depolarization field arising from an incomplete screening of surface charges, the out-of-plane polarization of the material will disappear when the film thickness is less than a few nanometers.This becomes a major obstacle for the scaling of ferroelectric-based devices.
In recent years, In 2 Se 3 has attracted much attention as an emerging two-dimensional (2D) III-VI ferroelectric semiconductor material.Ding et al. 9 predicted that the single-layer In 2 Se 3 exhibits room-temperature ferroelectricity with reversible spontaneous electric polarization in both out-of-plane and in-plane orientations.Distinct from other 2D and conventional bulk ferroelectric materials, In 2 Se 3 exhibits intrinsically inter-correlated in-plane and out-of-plane polarizations, and the reversion of the out-of-plane polarization by a vertical electric field also causes the rotation of the in-plane polarization 10 .Due to the non-centrosymmetry originating from the hexagonal stacking, the co-existence of in-plane and out-of-plane piezoelectricity also occurs in α-In 2 Se 3 ultrathin crystals 11 .Wan et al. 12 observed the Schottky barrier at the graphene/α-In 2 Se 3 interface that can be effectively tuned by switching the electric polarization under an applied voltage.2D In 2 Se 3 -based field effect transistors (FETs) have been demonstrated with high ON/OFF ratio of 10 8 and on-state current of 671 μA·μm −113 .Poh et al. 14 designed an asymmetric ferroresistive memory device to exploit the 2D semiconductor ferroelectric properties of α-In 2 Se 3 and achieved outstanding performances, with a giant electroresistance ratio of 3.9 × 10 6 and a readout current density of > 12 A/cm 2 , which enables the convenient fabrication of high-performance ferroelectric Schottky diode memory applications.
In semiconductor devices, metal-semiconductor (MS) junctions/interfaces play a pivotal role 15,16 .One strategy produces asymmetric current via metal-semiconductor-metal (MSM) structures, which consists of two MS junctions with distinct Schottky barriers connected back to back 17,18 .One Schottky barrier MS interface in the MSM structure is forward biased when a non-zero bias voltage is applied, while the other one is reversed biased.Predictably, the asymmetric MSM structure can be achieved when polar materials are contacted with the same metal.
In this paper, the interface properties and electron transport properties of α-In 2 Se 3 /Au contacts with different polarization directions are systematically investigated.Our results show that the α-In 2 Se 3 /Au contact can be switched from n-type to p-type Schottky contact when α-In 2 Se 3 polarization direction is reversed from upward to downward.Moreover, our transport calculations show that the intrinsic dipole results in asymmetric I-V characteristics, further underscoring the asymmetry of the MSM structure.The results provide helpful insights in the future design and fabrication of α-In 2 Se 3 -based new-concept devices.

Computational method and model
The calculations are performed using the projector-augmented wave (PAW) 19 pseudopotential and the plane wave cutoff energy of 400 eV as implemented in the Vienna ab initio simulation package (VASP) 20,21 .The Perdew-Burke-Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA) is used to describe the exchange-correlation interaction 22 .The Brillouin-zone integration is performed by using the 5 × 5 × 1 Monkhorst-Pack k-mesh and a Gaussian smearing broadening of 0.05 eV is adopted.The crystal lattice are relaxed to the ground state using a conjugate gradient algorithm.The total energy is converged to less than 1.0 × 10 −5 eV and the maximum force is less than 0.02 eV/Å during optimization.A 15 Å vacuum layer is adopted in the z direction to avoid interaction between periodic slabs.The long-range van der Waals (vdW) forces in α-In 2 Se 3 / Au contacts are described by the DFT-D2 method of Grimme 23 .
Transport simulations are performed using the QuantumATK 2015 package 24 to perform the density functional theory (DFT) coupled with non-equilibrium Green's function (NEGF) method 25,26 .The two-probe model is applicable to study the Schottky barrier in the transmission system in a FET.Here, a 5 nm freestanding singlelayer α-In 2 Se 3 is set as the channel (both up/down directions of single-layer α-In 2 Se 3 are taken into considerations) and α-In 2 Se 3 /Au interfacial system is considered as the electrode 27 .The periodic, Neumann, and Dirichlet boundary conditions are used in the x, y, and z directions of the device, respectively.In x direction, the single layer α-In 2 Se 3 is selected and a 15 Å vacuum layer is adopted to avoid interaction between periodic slabs.The lattice constant is 7.630 Å in y direction and the gate length of 66.075 Å is selected in z direction.The transmission coefficient T k (E) is obtained from the Green's function as follows: where k is set as a the reciprocal-lattice vector point along a surface-parallel direction which is also orthogonal to the transmission direction in the irreducible Brillouin zone (IBZ).G k (E) and G k † (E) represent the retarded and advanced Green's functions, respectively.Based on the self- ) describes the spectral function of the left and the right electrodes, respectively 28 .Single-ξ polarized (SZP) basis set is employed for high accuracy.The electronic structures of the electrodes and central region are calculated with a Monkhorst-Pack 50 × 50 × 1 and 1 × 50 × 1 k-point grids, respectively.The real-space mesh cutoff is set to 150 Ry.
In the single-layer α-In 2 Se 3 , the five atomic sublayers are arranged in sequence of Se-In-Se-In-Se in the out-of-plane direction, while atoms are arranged in a triangular lattice in each atomic sublayer, as shown in Fig. 1a.The optimized lattice constant of single-layer α-In 2 Se 3 is a = 3.986 Å, which is consistent with previous studies 29 .The polarization direction of α-In 2 Se 3 is defined by the direction of the built-in electric field.We (1)

Results and discussion
The α-In 2 Se 3 /Au structure has been fully optimized to obtain the energetically favorable configuration.During the process, the strain due to the lattice mismatch between the two layers is released by a small adjustment of the atomic configuration.The equilibrium interlayer distance (d z ) is the average distance between the closest layer of α-In 2 Se 3 and Au in the vertical direction.d Se-M is set as the minimum distance between the selenium atoms in α-In 2 Se 3 layer and the atoms in the Au layer.The binding energy ( E b ) of the α-In 2 Se 3 /Au contact is defined as: where E In 2 Se 3 , E Au and E In 2 Se 3 /Au represent the total energies of the α-In 2 Se 3 layer, Au layer, and α-In 2 Se 3 To gain further insight into interfacial properties, the plane-averaged charge density difference is calculated as follows: where ρ In 2 Se 3 /Au , ρ In 2 Se 3 , and ρ Au are the charge densities of the α-In 2 Se 3 /Au contact, single-layer α-In 2 Se 3 , and Au layer, respectively.Figure 2a,b show the charge density difference of Up-In 2 Se 3 /Au and Dw-In 2 Se 3 /Au contacts, respectively.Apparently, charge transfer occurs near the interface of α-In 2 Se 3 contacted with Au, indicating the formation of interfacial dipole.Bader charge analysis shows that the charge transfer in Up-In 2 Se 3 /Au contact (4.455 × 10 −3 e/Å 2 ) is larger than that in Dw-In 2 Se 3 /Au contact (3.518 × 10 −3 e/Å 2 ), as listed in Table 1.The result is in accordance with the interlayer distance and binding energy.
The tunneling barrier is crucial to the electrical properties of the semiconductor/metal contact.The tunneling barrier height, TB, eff , is defined as the lowest barrier to be overcome by the electrons from Au to the α-In 2 Se 3 , calculated as the potential difference between interface ( inter ) and the potential energy of α-In 2 Se 3 ( In 2 Se 3 ) 30,31 .The In 2 Se 3 is higher than inter in Up-In 2 Se 3 /Au contact, indicating no tunneling barrier exists, as shown in Fig. 2c.However, TB, eff of the Dw-In 2 Se 3 /Au contact is 0.102 eV, as show in Fig. 2d.
Figure 3  L,T (eV) and h L,T (eV) are the lateral electron (hole) Schottky barrier height (SBH) obtained from the quantum transport simulation.E g (eV) is the transport band gap of the FET. a DFT value from ref. 27 .b DFT value from ref. 30 .In the above electronic structure calculation, the electronic properties of the electrode region and channel are treated separately, ignoring the coupling between the two regions.A more reliable approach to study transistor SBH is to use the DFT-coupled NEGF method within a two-probe model, where the composite electrode (α-In 2 Se 3 /Au heterostructure) and the channel semiconductor are calculated as a whole, taking into account the coupling between the electrode region and the channel.As shown in Fig. 5a,b, the two-probe models of Up-and Dw-In 2 Se 3 FETs are constructed with symmetric MSM structure, respectively.Charge injected from Au electrodes to the channel α-In 2 Se 3 come across two interfaces (A and B): interface A is between the Au and α-In 2 Se 3 layer under the metal electrodes; interface B is between the α-In 2 Se 3 layer under the metal electrodes and the channel α-In 2 Se 3 layer.α-In 2 Se 3 undergoes metallization owing to a relative strong interaction with Au electrode, so there is no Schottky barrier V in the vertical direction and only Schottky barrier L in the lateral direction.

System
In general, there are two methods to calculate the transverse SBH.One is the work function approximation (WFA) and the other is the quantum transport simulation (QTS).In WFA, the electron (hole) SBH is simply calculated as the difference between the Fermi level value of the composite electrode and the CBM (VBM) value of the α-In 2 Se 3 channel.A transverse n-type Schottky contact is formed between Up-In 2 Se 3 /Au with an electron SBH of -0.530 eV, and a transverse p-type Schottky contact is formed between Dw-In 2 Se 3 /Au with a hole SBH of 0.393 eV.In WFA, the electrode-channel coupling is neglected.In contrast, the QTS method takes into account the electrode-channel coupling, so the method is a more reliable way to calculate the Schottky barrier.
Localized device density of states (LDDOS) is a direct method of reflecting the real space energy-band distribution in FETs, and the LDDOS of Up-and Dw-In 2 Se 3 transistors under zero gate and drain bias are shown  Figure 6a shows Au/α-In 2 Se 3 /Au FET with asymmetric MSM structure, which has two contacts: Up-In 2 Se 3 / Au (left) and Dw-In 2 Se 3 /Au (right).Since Up-In 2 Se 3 /Au and Dw-In 2 Se 3 /Au exhibit different SBH, this structure yields asymmetric I-V characteristic.Figure 6b shows that the backward current I ds (150 nA under − 1 V) is one order of magnitude larger than the forward current I ds (10 nA under 1 V).Therefore, the Au/α-In 2 Se 3 /Au FET with asymmetric structure exhibits remarkable rectification performance.At negative voltage, electrons drift from source to drain, crossing the n-type barrier of Up-In 2 Se 3 /Au, while holes drift in the opposite direction and cross the p-type barrier of Dw-In 2 Se 3 /Au.At a positive voltage, the potential barriers for electrons and holes increase.Figure 6c shows that under positive bias, the I ds varies slightly with increasing temperature.Under negative bias, the I ds has a much greater sensitivity to temperature.The results indicate a different transport mechanism between forward and reverse carrier transport in the MSM structure.To discern the transport mechanisms contributing to the current under each condition, Fig. 6d-f plot LDDOS at bias voltages 0 V and ± 1 V, respectively.It can be seen that the conduction and valence bands at the metal-semiconductor interface tend flat [Fig.1e and left illustration in Fig. 1b], indicating that the carrier transport under negative bias (− 1 V) is mainly through thermionic excitation 32 .On the contrary, the conduction and valence bands near the interface bend downward with the barrier becoming sharp under positive bias (1 V) [Fig.1f and right illustration in Fig. 1b], indicating that the carrier transport under positive voltage is mainly induced by tunneling 33 .

Conclusions
In conclusion, we investigate the interface and transport properties of the Up-and Dw-In

Figure 1 .
Figure 1.(a) Top and side views of the crystal structure of α-In 2 Se 3 .(b) Side views of α-In 2 Se 3 /Au contacts with two different ferroelectric polarization directions.

Table 1 .
shows the projected density of states (PDOS) of the freestanding single-layer α-In 2 Se 3 and Up-and Dw-In 2 Se 3 /Au contacts.The conduction band portion of bulk α-In 2 Se 3 is mainly contributed by In s and In p, (2) E b = (E In2Se3 + E Au − E In 2 Se 3 /Au )/N (3) �ρ = ρ In 2 Se 3 /Au − ρ Au − ρ In 2 Se 3 Calculated interfacial properties of α-In 2 Se 3 on Au surfaces.The lattice constant mismatches are given.The interlayer distance d z is the averaged distance between the surface Se atoms of α-In 2 Se 3 and the lowest Au layer in the z direction.The minimum distance d Se-M is the distance between the topmost Se atom of α-In 2 Se 3 and lowest Au atom.E b is the binding energy per unit cell of α-In 2 Se 3 .Δρ is the charge transfers from Au layer to α-In 2 Se 3 layer in Up-and Dw-In 2 Se 3 /Au contacts.W Au (eV) and W Se-Au (eV) are the work functions of Au and the α-In 2 Se 3 /Au systems.e while the valence band portion is mainly contributed by In p and Se s.Compared with the independent α-In 2 Se 3 , the E F of the Up-In 2 Se 3 /Au heterostructure can be found to be shifted in the direction of the conduction band, but the E F of the Dw-In 2 Se 3 /Au heterostructure is shifted toward the valence band.The indirect band gap of the freestanding monolayer α-In 2 Se 3 is 0.843 eV, and the valence band maximum (VBM) of α-In 2 Se 3 is located between the Γ and M points in the first Brillouin zone, while the conduction band minimum (CBM) is located at the Γ point, which is consistent with previous theoretical results9 , as shown in Fig.4a.Figure4shows the energy band structures of (b) Up-In 2 Se 3 /Au and (c) Dw-In 2 Se 3 /Au heterostructures.The blue and gray colors represent the contributions from the α-In 2 Se 3 and Au layers, respectively.Compared with pristine α-In 2 Se 3 , the energy bands of α-In 2 Se 3 hybridize with Au metal to some extent, but most of the α-In 2 Se 3 energy bands and Au energy bands can be identified by different colors.It can be found that the Up-In 2 Se 3 energy band structure is significantly more hybridized than Dw-In 2 Se 3 , which is consistent with the strong interfacial forces analyzed previously.The energy band structure of α-In 2 Se 3 is all disrupted and the Fermi energy level crosses the α-In 2 Se 3 -dominated energy band, indicating that α-In 2 Se 3 undergoes metallization in all these interfacial systems.

Figure 2 .
Figure 2. Electronic structure at the interface between α-In 2 Se 3 and Au.∆ρ is the planar average charge density difference between α-In 2 Se 3 and Au.V eff is the electrostatic potential along the z-direction for α-In 2 Se 3 contacted with Au. (a,c) for Up-In 2 Se 3 /Au contact, as well as (b,d) for Dw-In 2 Se 3 /Au contact.

Figure 3 .
Figure 3. Projected density of states (PDOS) of α-In 2 Se 3 contacted with Au.(b) Up-In 2 Se 3 /Au and (c) Dw-In 2 Se 3 /Au.The Fermi level E F is set at 0 eV and indicated by the black vertical dashed line.(a) The PDOS of freestanding monolayer α-In 2 Se 3 is provided for comparison.

Figure 4 .
Figure 4. Band structure of of α-In 2 Se 3 contacted with Au.(b) Up-In 2 Se 3 /Au and (c) Dw-In 2 Se 3 /Au.The Fermi level is set to zero energy.The blue line indicates the energy band structure of the α-In 2 Se 3 projection, whose weight is represented by the size of the dot.(a) The band structure of freestanding monolayer α-In 2 Se 3 is provided for comparison.

Figure 5 .
Figure 5. Transport properties of α-In 2 Se 3 /Au field-effect transistor with a channel length of 5 nm.Schematic cross-sectional view of (a) Up-In 2 Se 3 /Au and (b) Dw-In 2 Se 3 /Au.The red and black arrows show the pathway of electron injection from Au to α-In 2 Se 3 at interfaces A and B, respectively.V and L represent the SBH in the vertical and lateral direction, respectively.Local device density of states (LDDOS) and transmission spectra of (c) Up-In 2 Se 3 /Au and (d) Dw-In 2 Se 3 /Au under zero bias.

2 Figure 6 .
Figure 6.Transport properties of the asymmetric Au/α-In 2 Se 3 /Au FET and transport mechanism.(a) Scheme of the asymmetric Au/α-In 2 Se 3 /Au FET.(b) The corresponding I-V characteristic curve of this device.The illustrations are schematic band diagrams under negative (left) and positive (right) bias voltages, respectively.(c) The current versus temperature from 50 to 300 K of this device under different bias voltages.(d-f) LDDOS of this device at the bias voltage 0 V, − 1 V and 1 V, respectively.
/Au het- erostructure, respectively.The total number of unit cells of α-In 2 Se 3 in the system is represented by N. According to this definition, positive values denote favorable interface binding.As shown in Table 1, the d z and d Se-M are 2.523 Å (2.665 Å) and 2.643 Å (2.697 Å) for Up-In 2 Se 3 /Au (Dw-In 2 Se 3 /Au) contact, respectively, and they are comparable with the covalent bond length of Au-Se (2.56 Å).While for the isolated Au (5d 10 6s 1 ) atoms, the outermost orbital is occupied by only one unpaired s, which leads to a relatively strong E b because only one covalent bond will be formed between Au and α-In 2 Se 3 .Furthermore, the E b are 0.962 eV and 0.822 eV for Up-In 2 Se 3 and Dw-In 2 Se 3 contacted with Au, respectively.